UPDATE #2 June 16 2011: Caroline Katsam has sent us a new paper that has been accepted for publication which addresses the issue of how long lack of warming in the upper ocean should be expected based on the model predictions. The paper is

“Over the period 2003–2010, the upper ocean has not gained any heat, despite the general expectation that the ocean will absorb most of the Earth’s current radiative im- balance. Answering to what extent this heat was transferred to other components of the climate system and by what process(-es) gets to the essence of understanding climate change. Direct heat flux observations are too inaccurate to assess such exchanges. In this study we therefore trace these heat budget variations by analyzing an ensemble of climate model simulations. The analysis reveals that an 8-yr period without upper ocean warming is not exceptional. It is explained by increased radiation to space (45%), largely as a result of El Niño variability on decadal timescales, and by increased ocean warming at larger depths (35%), partly due to a decrease in the strength of the Atlantic meridional overturning circulation. Recently-observed changes in these two large-scale modes of climate variability point to an upcoming resumption of the upward trend in upper ocean heat content.”

I will have more to say on this paper in a later post. However, the attribution of the missing heat to El Niño and to deeper transport into the ocean misses that El Niño itself is part of the climate system and deeper heating would have to transit the upper ocean where it would have been seen (but, apparently was not) in the Argo and other data sets .

Bob Tisdale has alerted me to an error in my computation of ocean heat content in Joules from that post where I used a conversion from Watts per meter squared to Joules per decade with respect to the upper ocean that was missing a multiplier of 0.7 to account for the fractional area of the ocean with respect to the total heating of the climate system in Joules.

I am reposting the relevant part of the 2009 post with the correction and updating this post with the latest information. It has now been at least since 2003 that there has not be significant heating of the upper ocean.

“I do agree with you that several years of zero or little radiative imbalance poses some very difficult questions for the modeling community. But I do not think it is grounds for outright rejection of all model results.”

Joules resulting from a positive radiative imbalance must continue to be accumulated in order for global warming to occur. In the last 7 1/2 years there has been an absence of this heating. An important research question is how many more years of this lack of agreement with the GISS model (and other model) predictions must occur before there is wide recognition that the IPCC models have failed as skillful predictions of the effect of the radiative forcing of anthropogenic inputs of greenhouse gases and aerosols.

The use of the ocean heat content change as the most appropriate metric to diagnose global warming was reported in

“Our climate model, driven mainly by increasing human-made greenhouse gases and aerosols among other forcings, calculates that Earth is now absorbing 0.85±0.15 W/m2 more energy from the Sun than it is emitting to space. This imbalance is confirmed by precise measurements of increasing ocean heat content over the past 10 years.”

“The decadal mean planetary energy imbalance, 0.75 W/m2, includes heat storage in the deeper ocean and energy used to melt ice and warm the air and land. 0.85 W/m2 is the imbalance at the end of the decade.”

Thus, the best estimate value of 0.60 Watts per meter squared given in Hansen et al can be used, as a conservative value, to calculate the heat change in Joules that should be expected in the upper ocean data from 2003 to the present.

The observed best estimates of the heating and the Hansen et al prediction in Joules in the upper 700m of the ocean are given below:

OBSERVED BEST ESTIMATE OF ACCUMULATION Of JOULES [assuming a baseline of zero at the end of 2002].

Thus, according to the GISS model predictions, there should have been approximately 5.36 * 10**22 Joules more heat in the upper 700 meters of the global ocean at the end of 2010 than were present at the beginning of 2003.

For the observations to come into agreement with the GISS model prediction by the end of 2012, for example, there would have to be an accumulation 6.7 * 10** 22 Joules of heat over just the next 1 1/2 years. This requires a heating rate over the next 1 1/2 years into the upper 700 meters of the ocean corresponding to a radiative imbalance of ~4 Watts per square meter.